Starting from the primitive equations[1]}, the continuity
and zonal momentum equations in spherical coordinates are
\(\frac{\partial \rho }{\partial t}+\rho \left(\frac{1}{R_{{\rm J}}\cos \vartheta }\frac{\partial u}{\partial \lambda }+\frac{1}{R_{{\rm J}}\cos \vartheta }\frac{\partial }{\partial \vartheta }\left(v\cos \vartheta \right)+\frac{\partial w}{\partial r}\right)+\frac{u}{R_{{\rm J}}\cos \vartheta }\frac{\partial \rho }{\partial \lambda }+\frac{v}{R_{{\rm J}}}\frac{\partial \rho }{\partial \vartheta }+w\frac{\partial \rho }{\partial r}=0,\) 
